I’ve been bicycling for years but just recently purchased the Park Tool Chain Scrubber. This may be the simplest way to clean your bike chain and it can be done without dismantling anything (on most bikes).
The tool has evolved and been improved over the years from when I first saw it, with a smallish reservoir and three “spoke style” brushes, to what you see today. The first brush the chain encounters scrubs the outside of the links and the next two brush the inside and rollers. Before exiting the chain runs across a sponge to reduce the amount of cleaner remaining on it. There is a magnet in the bottom of the reservoir to pull the ferrous particles out of suspension and the entire thing comes apart for easy cleanup (strongly recommended to keep it working at its best).
Honestly, I can’t remember the last time I had this much “fun” cleaning a bike chain. Previously. to get a chain really clean. I would remove it from the frame and soak and brush before hanging to dry and then re-installing and adding chain lube.
The kit I purchased also comes with a hand brush that has a semi-circular toothed handle for digging the crud out from between the rear cogs and a bottle of citrus based cleaning solution. Support your local bike shop, ~ $30 or ~ $25 online + shipping.